ABSTRACT
Throughout this chapter, random samples drawn from known distributions where the unknown parameters that characterize these distributions will be of interest. To specify completely a probability distribution, whether it be discrete or continuous, the distribution’s parameters must be specified. For example, a random variable may follow a normal distribution; however, if both the mean and the standard deviation of the normal distribution are not known, the distribution at hand cannot be completely specified. In a similar fashion, a Poisson random variable requires knowledge of the parameter to specify that distribution completely. In general, the pdf of a random variable X is f(x |✓ ), where ✓ is the vector of parameters that characterize the pdf. The vector of parameters ✓ is defined over a parameter space denoted⇥ . For each value of ✓ 2 ⇥, there is a di↵erent pdf. To obtain possible values for the vector of parameters, a random sample from the population of interest is taken, and statistics called estimators are constructed. The values of the estimators are called point estimates. For example, X may be used as a point estimator for µ; in which case, x¯ is a point estimate of µ.
